A Practitioner's Approach to Estimating Intertemporal Relationships Using Longitudinal Data: Lessons from Applications in Wage Dynamics

This chapter presents a unified set of estimation methods for fitting a rich array of models describing dynamic relationships within a longitudinal data setting. The discussion surveys approaches for characterizing the micro dynamics of continuous dependent variables both over time and across individuals, focusing on two flexible sets of empirical specifications: dynamic simultaneous equations models incorporating error-components structures, and autoregressive quantile models. The chapter is motivated by the principle that, whenever possible, estimation methods should rely on routines available in familiar software packages to make them accessible to a wide range of practitioners. Conventional method-of-moments procedures offer a general apparatus for estimating parameters of panel-data specifications, though one must introduce a series of modifications to overcome challenges arising from: (1) use of unbalanced data structures, (2) weighting to account for stratified sampling inherent in survey longitudinal data, (3) incorporation of predetermined variables in estimation, and (4) computational complexities confronted when estimating large systems of equations with intricate intertemporal restrictions. To allow researchers to separate the estimation of longitudinal time-series specifications into manageable pieces, the discussion describes multi-step approaches that estimate subsets of parameters appearing in a single model component (such as the autoregressive or moving-average structure of the error process) without having to estimate all parameters of the entire model jointly. Such procedures offer a powerful set of diagnostic tools for narrowing model choices and for selecting among specifications that fit the underlying data. To illustrate all of the econometric methods outlined in this chapter, the analysis presents a set of empirical applications summarizing the dynamic properties of hourly wages for adult men using data from the Panel Study of Income Dynamics.